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Article Dans Une Revue Compositio Mathematica Année : 2016

The Brauer group and indecomposable -cycles

Bruno Kahn

Résumé

We show that the torsion in the group of indecomposable $(2,1)$-cycles on a smooth projective variety over an algebraically closed field is isomorphic to a twist of its Brauer group, away from the characteristic. In particular, this group is infinite as soon as $b_2-\rho>0$. We derive a new insight into Roitman's theorem on torsion $0$-cycles over a surface.

Dates et versions

hal-02740626 , version 1 (02-06-2020)

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Bruno Kahn. The Brauer group and indecomposable -cycles. Compositio Mathematica, 2016, 152 (5), pp.1041-1051. ⟨10.1112/S0010437X15007733⟩. ⟨hal-02740626⟩
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